The experimental advances have been boosting the theoretical investigation, by pushing the application of canonical methods as well as the development of novel techniques aiming at providing the most accurate description of the dynamics of coalescing binary systems.
Earlier developments dedicated to the post-Newtonian (PN) [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]},
and the post-Minkowskian (PM) approximation [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]},
the gravitational self-force formalism [27]}, [28]},
the effective–one-body formalism [29]}, [30]},
as well as the effective field theory (EFT) approach
for the PN formulation of general relativity
 [31]}, [32]}, [33]},
have been flanked by modern Feynman diagrams-
[34]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}, [41]}, [42]}, [43]}, [44]},
and Scattering Amplitudes-based approaches [45]}, [46]}, [47]}, [48]}, [49]}, [50]}, [51]}, [52]}, [53]}, [54]}, [55]}, [56]}, [57]}, [58]}, [59]}, [60]}, [61]}, [62]}, [63]},
which turned out to be particularly powerful for the determination of the perturbative corrections to the classical potential within the EFT approach.
